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We present a density functional theory (DFT) calculation in the generalized gradient approximation to study the possibility for the existence of Jahn-Teller (JT) or pseudo Jahn-Teller (PJT) type local distortions in the La-Ba-Cu-O superconducting system. We performed the calculation and correspondingly group theory classification of the electronic ground state of the CuO6 elongated octahedra cluster, immersed in a background simulating the superconductor. Part of the motivation to do this study is that the origin of the apical deformation of the CuO6 cluster is not due to a pure JT effect, having therefore a non a priori condition to remove the degeneracy of the electronic ground state of the parent regular octahedron. We present a comparative analysis of the symmetry classified electron spectrum with previously reported results using unrestricted Hartree-Fock calculations (UHF). Both the DFT and UHF calculations produced a non degenerate electronic ground state, not having therefore the necessary condition for a pure JT effect. However, the appearance of a degenerate Eg state near to the highest occupied molecular orbital in the DFT calculation, suggests the possibility for a PJT effect responsible for a local distortion of the oxidized CuO 6 cluster.